It was a clash of ideology. Democratic politico Howard Dean accidentally backed his SUV into Republican power player Georgette Mosbacher’s brand-new Lexus sedan last night as he tried to edge out of a parking spot on the Upper West Side, a source told The Post. Mosbacher’s chauffeur was waiting to pick up the cosmetics mogul for a dinner with the Rwandan ambassador at 6:15 p.m. when the former Vermont governor’s Jeep Cherokee gave him a jolt. Dean’s jaw dropped when the driver handed over the car’s registration papers. “He couldn’t believe it when he found out it belonged to Georgette,” the source recalled. “He was very gracious about the whole thing and promised to pay for the damage.” Mosbacher’s sedan suffered minor bumper damage, while the 2004 presidential candidate’s Jeep came away unscathed. “Georgette thought it was a pretty funny circumstance,” the source said. “The car was fine — just a few scratches — and she made it to her dinner.” A co-chairperson for John McCain’s 2008 presidential campaign, Mosbacher is considered one of Mitt Romney’s most influential fund-raisers, while Dean has emerged as a vocal critic of the Massachusetts Mormon.